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Unformatted text preview: xy = 1, the xaxis, and the two lines x = 1 and x = 2. Choose the order of integration which makes the limits simplest. Problem 2. The picture shows the portion of the solid formed by the intersection of the solid cylinders y 2 + z 2 1 and x 2 + z 2 1 (two cylinders of radius 1, centered on the xaxis and on the yaxis respectively) which lies in the Frst octant ( x 0, y 0, z 0). (The front face is a portion of the cylinder x 2 + z 2 = 1, while the right face is part of the cylinder y 2 + z 2 = 1.) ind the volume and the centroid ( x, y, z ) (= center of mass with uniform density = 1) of the pictured solid. (Hint: the integral is easier to set up in the order dx dy dz )....
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 Fall '07
 Hutchings
 Integrals

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